Question

You are about to be dealt a 5-card poker hand from a well-shuffled deck.  What is the...

You are about to be dealt a 5-card poker hand from a well-shuffled deck.  What is the probability that your hand will contain exactly one diamond?

a. 0.20

b. 0.00005

c. 0.41

d. 0.19

Math   Statistics-And-Probability   
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Answer #1

Number of ways to choose 5-card poker hand from a well-shuffled deck of 52 cards is,

= 2598960

Number of ways to choose one diamond from 13 diamonds in well-shuffled deck is 13.

Number of ways to choose remaining 4 cards from remaining 39 non-diamond card in well-shuffled deck is

= 82251

Probability that your hand will contain exactly one diamond = Number of ways to choose one diamond * Number of ways to choose remaining 4 cards / Number of ways to choose 5-card poker hand

= (82251 * 13) / 2598960

= 0.41

c. 0.41

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